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Frequency-chirped readout of spectral features from spatial-spectral (S2) materials, as a result of spectral hole-burning, has been in use as a radio-frequency (RF) spectrum analyzer for well over a decade. Previously, a signal processing deconvolution algorithm had been developed that enabled faster chirping, such that the chirp rate 'K' could be much greater than the desired resolution bandwidth (RBW). This broke past conventional limits for spectroscopic detection, which states that one needs to dwell on a spectral feature of width gamma for a time 1/gamma. For a chirp, this would mean that the square root of the chirp rate would need to be less than the RBW. For chirp rates on the order of gamma 2 or higher, nonlinearities begin to appear in detected signals depending on optical absorption depth, the chirp rate, and burned hole depths. Even with this algorithm, distortions still persist when very deep holes are burned in a high absorbing material, while the chirp rate is still very high. However, resolving spectral features under these conditions is desirable to increase the dynamic range of the SA. A new nonlinear signal processing technique that removes the nonlinearity has been developed, recovering the distorted signals. It was applied to RF signals spectrally absorbed in two different Tm 3+: YAG crystals, with measured absorption lengths of 1.9 and 2.5. The new algorithm is shown to work on multiple spectral holes simultaneously. Signals as wide as 1 MHz and as small as 300 kHz were recovered for a chirp rate of about 11.88 MHz/microsecond. These results show that very fast chirp rates could be used for highly absorbing materials, with deeply burned spectral holes. This could enable ultra-sensitive readout of a spectrum spanning hundreds of gigahertz, while pushing the dynamic range higher.